

A072296


Least number starting a chain of exactly n consecutive even integers that do not have cototientinverses.


2



10, 50, 532, 2314, 4628, 22578, 115024, 221960, 478302, 3340304, 22527850, 117335136, 1118736102, 1564578508, 6121287812, 7515991946
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OFFSET

1,1


COMMENTS

If the strong Goldbach conjecture (every even number>6 is the sum of at least 2 distinct primes p and q) is true, sequence contains only even values. Since p*qphi(p*q)=p+q1 and then every odd number can be expressed as xphi(x).  Benoit Cloitre, Mar 03 2002.


LINKS



EXAMPLE

Neither 50 nor 52 have cototientinverses and since 50 is the first of the two and the least number with this property, a(2) = 50.


MATHEMATICA

a = Table[0, {5*10^7}]; Do[b = n  EulerPhi[n]; If[ b < 5*10^7 + 1, a[[b/2]]++ ], {n, 2, 615437100}] (* used to find a(7) *) Do[ If[ a[[n]] == a[[n + 1]] == a[[n + 2]] == a[[n + 3]] == a[[n + 4]] == a[[n + 5]] == a[[n + 6]] == 0, Print[n]], {n, 1, 10^6}]


CROSSREFS



KEYWORD

hard,more,nonn


AUTHOR



EXTENSIONS



STATUS

approved



